Subgroups — C₄₇×#63118⋊C₃ #49144017

Order 36660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₇×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#63118	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃⋊C₃×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₇×AGL(1,𝔽₁₃)	—	5	1	no	maximal, Hall
5	C₅×D₁₃×C₄₇	C₂×C₃	1	1	yes	characteristic
6	C₄₇×D₁₃⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×Dic₅×C₄₇	—	13	1	no	maximal, Hall
9	C₄₇×#261	—	5	1	no	Hall
10	C₁₃⋊C₃×C₄₇	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₇	—	13	1	no	—
12	D₁₃×C₄₇	C₃×D₅	1	1	yes	characteristic
13	Dic₅×C₄₇	—	13	1	no	Hall
14	#63118⋊C₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₇	—	13	1	no	Hall
16	C₁₃×C₄₇	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄×C₄₇	—	65	1	no	Hall
18	C₂×C₅×C₄₇	—	13	1	no	—
19	C₅×D₁₃⋊C₃	C₂×C₄₇	1	1	yes	characteristic
20	C₂×C₃×C₄₇	—	13	1	no	—
21	#63118	C₃×C₄₇	1	1	yes	characteristic, complemented, Hall
22	C₅×C₄₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₃⋊C₃	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
24	C₄×C₄₇	—	65	1	no	Hall
25	AGL(1,𝔽₁₃)	—	5	1	no	Hall
26	C₃×C₄₇	—	13	1	no	Hall
27	C₅×D₁₃	C₂×C₃×C₄₇	1	1	yes	characteristic
28	C₂×C₄₇	—	13	1	no	—
29	D₁₃⋊C₃	D₅×C₄₇	1	1	yes	characteristic
30	C₅×C₁₃	C₃×C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
31	C₃×Dic₅	—	13	1	no	Hall
32	#261	—	5	1	no	Hall
33	C₄₇	#63118⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₁₃⋊C₃	Dic₅×C₄₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	13	1	no	—
36	D₁₃	C₃×D₅×C₄₇	1	1	yes	characteristic
37	Dic₅	—	13	1	no	Hall
38	C₃×C₅	—	13	1	no	Hall
39	C₁₃	C₃×Dic₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	65	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₄₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	65	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₄₇	#63118⋊C₃
commutator, hypocenter	C₅×C₁₃	C₃×C₄×C₄₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₄₇	C₃×C₄
prime radical	C₅×C₄₇×D₁₃⋊C₃	C₂
cosocle	C₅×D₁₃	C₂×C₃×C₄₇
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₄₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄₇×#63118	C₃	semidirect
3. C₅×C₁₃⋊C₃×C₄₇	C₄	semidirect
7. C₅×C₁₃×C₄₇	C₃×C₄	semidirect
10. C₁₃⋊C₃×C₄₇	Dic₅	semidirect
14. #63118⋊C₃	C₄₇	direct (N × H)
16. C₁₃×C₄₇	C₃×Dic₅	semidirect
21. #63118	C₃×C₄₇	semidirect
22. C₅×C₄₇	AGL(1,𝔽₁₃)	semidirect
23. C₅×C₁₃⋊C₃	C₄×C₄₇	semidirect
30. C₅×C₁₃	C₃×C₄×C₄₇	semidirect
33. C₄₇	#63118⋊C₃	direct (N × H)
34. C₁₃⋊C₃	Dic₅×C₄₇	semidirect
39. C₁₃	C₃×Dic₅×C₄₇	semidirect
43. C₅	C₄₇×AGL(1,𝔽₁₃)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₄₇×D₁₃⋊C₃	2
C₄₇×#63118	3
C₄₇×AGL(1,𝔽₁₃)	5
C₃×Dic₅×C₄₇	13
#63118⋊C₃	47

Subgroups — C47×#63118⋊C3 #49144017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#63118⋊C₃ #49144017